Rationality, Logic, Paradox, and Paraconsistency

Types of logic: classical, basic modal, normal modal, non-normal, conditional, intuitionist, many-valued, first degree entailment, basic relevant, mainstream relevant, and fuzzy logic.

Priest's book:
http://www.amazon.com/Introduction-Non-Classical-Logic-Graham-Priest/dp/05217...

True Contradictions:
http://plato.stanford.edu/entries/logic-paraconsistent/#DiaTruCon

http://plato.stanford.edu/entries/dialetheism/

Category:

Education

Tags:

• philosophy
• elimisteve
• logic
• consistent
• paraconsistent
• paradox
• rational
• rationality

[boshea8498]

thought about this the other day. so lets write the liar sentence in the form

g= g is false.

g being the liar sentence.

Next plug in for g, on the right handside, the definition of g.

We get g = (g is false) is false.

Do the 'same' thing again. g = ((g is false) is false) is false.

We can do this forever. therefore the statement has no definite form. and the statement can never really be stated. From this perspective the statement can be viewed as non-sense?

or could call all forms equivalent?

[Paraconsistant]

@CammieSpectrum I tried to avoid discussion of truth bearers and truth makers because it would introduce unnecessary complication. But suffice it to say that, like Quine and many others, I don't believe in 'meanings' or 'propositions' in the sense in which you have used the former. (In this way I am a deflationist.) That aside, I do not understand your proposed solution to the liar's paradox. Thank you for the discourse.

[CammieSpectrum]

@Paraconsistant a Sentence can't be True or False, my friend, only the Meaning of a Sentence, and then there are sentences that have no reference at all, like furious green ideas sleep furiouslly; I think that 98 percent of academics, are saying 'This Sentenceis a Lie', and don't realize that they are using It to mean, a Visual Impression of the Sentence, 'This Sentence of a Lie', like on a Page of a Document; I think that's how the confusion happens :)

[Paraconsistant]

@CammieSpectrum The liar's sentence asserts that it itself is false. Just as the other self-referential sentences which we discussed assert that it itself contains some property or feature. What is not meaningful about that? I should like to stress that you know exactly what it means, as a competent English user, which is why you seek to resolve the difficulty. Cammie, as yourself this: If you are right, then why have 98% of mathematicians, philosophers, and logicians disagreed with you here?

[CammieSpectrum]

@Paraconsistant The sentence,"This Sentence is a Lie' >>>>" The Meaning of this Sentence is a Lie". what's the meaning of this sentence????

[Paraconsistant]

@CammieSpectrum That nature does or does not contain contradictions is undetermined, I would say. Nevertheless, the sentence 'The first word in this sentence begins with the letter t' is perfectly meaningful, so, too, is the liar's sentence. In fact, you know exactly what it means because you seek to construct some means by which you can avoid the unpalatable conclusions which one might derive from such sentences.

[CammieSpectrum]

@Paraconsistant Proof would be that there are no contradictions in meanings, for their are not contradictions in nature; just because you can construct a sentence does not make it meaningful; and there are obviouslly many examples of this

[Paraconsistant]

@CammieSpectrum The first reply should read where appropriate: "In order to eradicate self-referring sentences from natural language, you will, in a non-arbitrary, non ad hoc manner, have to show precisely why..." Apologies for the typos.

[Paraconsistant]

@CammieSpectrum You may if you wish go along with Alfred Tarski and admit that natural languages are inextricably fraught with expressions which lead to antinomies, label natural languages as therefore hopelessly too imprecise to serve the needs of the logical exactness of exact logical precision, and go about formalizing what you can of natural language, but self-reference is here to stay. BTW: Check out Tarski's object language - metalanguage distinction; you may find it interesting.

[Paraconsistant]

@CammieSpectrum (1) refers to (2) which refers to (1), ergo, no self-referencing going on here. Listen, the point is this: In order to eradicate self-referring sentences a non-arbitrary, non ad hoc manner precisely why self-referring sentences ought not to be permitted. Self-referring sentences are unequivocally an unavoidable feature of natural languages. I.e. sentences like 'The first word in this sentence begins with the letter T' is simply true, and as users of English, we both know it.